The unstable strata \(S_\beta \)  can be inductively described following [1]}: first, pick a representative \(\lambda _\beta \)  of each conjugacy class \(\beta \)  (to do this canonically, fix a maximal torus \(T\)  and positive Weyl chamber \(\mathfrak {t}_+\)  in the Lie algebra \(\mathfrak {t}\)  of \(T\) , and then pick the representatives in \(\mathfrak {t}_+\) ). For any 1-PS \(\lambda \)  of \(G\) , there is a parabolic subgroup
\(P(\lambda ) : = \lbrace  g \in G : \lim _{t \rightarrow 0} \lambda (t) \: g \: \lambda (t)^{-1} \mathrm {\: exists \: in \: } G \rbrace ,\) 
